Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C73 ⋊ C4⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#10596842 |
| commutator | C2×C73 | C2×C32 |
| Fitting | C2×C8×C73 | C8 |
| socle | C22×C73 | C2×C16 |
| hypercenter | C2×C8 | #10596842 |
| hypocenter | C73 | C4⋊C32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^10,h^b=h^72,h^d=h^27,h^e=h^72224 conjugacy classes — view the full character table.
| maximal subgroup of | #34034423, C2×#22627030, #34034426, … |
| maximal normal subgroup of | #34034423, C2×#22627030, #34034426, … |
| maximal quotient of | #34033108, #34033116, #34033128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21609);